arXiv subjects

Francisco J. Gozzi

Publications and source records attributed to Francisco J. Gozzi.

5 recordsLinked to original sources

arXiv2026

Persistent Cost of Lipschitz Maps

A $1$-Lipschitz map between compact metric spaces $f\colon X\to Y$ induces a homomorphism of persistence modules on degree-$d$ Vietoris--Rips persistent homology. We define the persistent cost of $f$ from this induced homomorphism by quantifying the persistence carried by its kernel and cokernel modules. We prove that the persistent cost controls the interleaving distance between the degree-$d$ Vietoris--Rips persistent homology modules of $X$ and $Y$. Moreover, we obtain an explicit upper bound for the persistent cost in purely metric terms. Finally, we give a self-contained proof of the stability of the persistent cost introducing a Gromov-Hausdorff type distance for maps between compact metric spaces.

math.AT↗

arXiv2022

A Note On Polar Representations

We show how a polar representation of a compact connected Lie group can be linearly determined from its dimension and isotropy subgroup data in the general reducible case.

math.DG↗

arXiv2018

Representations of Compact Lie Groups of Low Cohomogeneity

We survey different tools to classify representations of compact Lie groups according to their cohomogeneity and apply these methods to the case of irreducible representations of cohomogeneity 6, 7 and 8.

math.RT↗

arXiv2017

Representations with $Sp(1)^k$-reductions and quaternion-Kähler symmetric spaces

We classify non-polar irreducible representations of connected compact Lie groups whose orbit space is isometric to that of a representation of a finite extension of $Sp(1)^k$ for some $k>0$. It follows that they are obtained from isotropy representations of certain quaternion-Kähler symmetric spaces by restricting to the "non-$Sp(1)$-factor".

math.DG↗

arXiv2014

Low Dimensional Polar Actions

Polar manifolds are Riemannian G-manifolds admitting a "section", i.e., a complete submanifold passing through every orbit and doing so orthogonally. We consider compact simply-connected polar manifolds and achieve an equivariantly diffeomorphic classification in dimensions 5 or less. As an application, we determine which of these polar actions admit an invariant metric with non-negative curvature.

math.DG↗